Question

At a certain restaurant, 8 sandwiches and 10 burritos will cost $123.40. In addition, 5 sandwiches

and 9 burritos cost $97.20. Assuming that we are talking about the same sandwiches and burritos,
what is the cost of 1 sandwich? What is the cost of 1 burrito? Let x represent the cost of a
sandwich and y represent the cost of a burrito
Equation #1:
Equation #2:
Cost of 1 burrito:
Cost of 1 sandwich: $

Answer 1

8x + 10y = 123.40

5x + 9y = 97.20

OR

40x + 50y = 617

-40x - 72y = -777.6

x = $6.30

y = $7.30

Explanation:

we can write this system of equations:

8x + 10y = 123.40

5x + 9y = 97.20

using the 'elimination method', we can multiply the first equation by 5 and the second equation by -8 to get:

5(8x + 10y) = 123.4(5)

40x + 50y = 617

-8(5x + 9y) = 97.2(-8)

-40x - 72y = -777.6

now we can add the new equations and solve for 'y':

40x + 50y = 617

-40x - 72y = -777.6

-22y = -160.6

y = 7.30

now we can substitute 7.3 for 'y' so we can solve for 'x':

8x + 10(7.3) = 123.4

8x + 73 = 123.4

8x = 50.4

x = 6.30

Answer 2

Equation 1: 8x + 10y = 123.4

Equation 2: 5x + 9y = 97.2

cost of a burrito = $7.30

cost of a sandwich = $6.30

Explanation:

Let x = cost of a sandwich

Let y = cost of a burrito

Equation 1: 8x + 10y = 123.4

Equation 2: 5x + 9y = 97.2

Rewrite equation 1 to make y the subject, then substitute into equation 2 and solve for x:

8x + 10y = 123.4

⇒ 10y = 123.4 - 8x

⇒ y = 12.34 - 0.8x

5x + 9(12.34 - 0.8x) = 97.2

⇒ 5x + 111.06 - 7.2x = 97.2

⇒ 13.86 = 2.2x

⇒ x = 6.3

So cost of a sandwich = $6.30

Substituting x = 6.3 into equation 2 and solving for y:

5(6.3) + 9y = 97.2

⇒ 31.5 + 9y = 97.2

⇒ 9y = 65.7

⇒ y = 7.3

So cost of a burrito = $7.30